For the data set 7,5,10,11,12 the mean is x, is 9. what is the standard deviation?

SD(σ)=2.91548

Step-by-step explanation:

Definition:

Standard deviation (SD) measures the volatility or variability across a set of data. It is the measure of the spread of numbers in a data set from its mean value and can be represented using the sigma symbol (σ)

To find out SD you must know the value of Mean and Variance.

Mean=sum of values / N (number of values in set)

Mean=7+5+10+11+12/5

Mean=45/5

Mean=9

Variance=((n1- Mean)2 + ... nn- Mean)2) / N-1 (number of values in set - 1)

Variance=((7-9)^2 +(5-9)^2+(10-9)^2+(11-9)^2+(12-9)^2))/5-1

Variance=((-2)^2+(-4)^2+(1)^2+(2)^2+(3)^2)/4

Variance=(4+16+1+4+9)/4

Variance=34/4

Variance=8.5

Standard Deviation(σ)=√Variance

σ = √8.5

By taking the square root of √8.5 we get;

σ = 2.91548

Thus the value of Standard Deviation(σ)=2.91548

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step-by-step explanation: